A Nonsimilar Solution for Multicomponent Reacting Laminar and Turbulent Boundary Layer Flows Including Transverse Curvature

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Abstract
A mathematical model of a multicomponent reacting nonsimilar laminar or turbulent boundary layer flow including transverse curvature effects is presented, and a method of solution is given. The formulation is an extension of an earlier work in which thermal and molecular diffusion were treated in terms of a bifurcation approximation for binary diffusion coefficients. In the present analysis, a turbulent model is added which employs a mixing length model for eddy viscosity in the wall region with consideration of injection or suction effects. The wake region eddy viscosity is taken to be proportional to the free stream velocity and local velocity defect thickness. Transverse curvature effects are also incorporated into the present analysis. A modification of the Levy-Lees transformation is used to transform the equations of motion to a coordinate plane, where the conservation equations are integrated across boundary layer strips. Derivatives in the normal direction are related to one another by Taylor series truncated to reflect a quadratic or cubic approximation, and streamwise derivatives are expressed in finite difference form. The resultant set of equations is solved by general Newton-Raphson iteration.

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